I just finished watching a PBS show about the life of Newton, called Isaac Newton's Dark Secrets in which they claimed Newton was an Arian (one who denied the deity of Christ and thus the Trinitarian belief of orthodox Christianity.) It is evident that Newton did in fact engage in alchemy and other, at the time, taboo pursuits, but it seems that much of this was early chemistry and scientific investigation, the consideration of Arianism, however was a much more dangerous pursuit.
Upon a bit of research I found a couple things. First, it is apparent from the discussions of Newton's theological research that he was questioning the deity of Christ. The PBS show mentioned that Newton 'scoured anchient texts' and had doubts about the inclusion of specific verses in the Canon. Of course, given the recent finds of more anchient manuscripts, it would seem that much of Newton's concerns would have been answered. Considering the content of Newton's argument, what little we know of it, it would seem that he'd yet to encounter a serious theological apologetic for the Trinity. PBS however seemed to indicate that Newton's possible Arian leanings were something positive, seemingly playing up the idea that Trinitarian beliefs are foreign to the text of Scripture and the early church (ala the Da Vinci Code.)
Newton's examination of Arianism is being used by various anti-Christian apologetics sites to support the idea that Newton, clearly one of the greatest scientific thinkers of all time denied basic orthodox doctrines. Do a quick Google of "Newton Arian" and note the number of anti-Trinitarian sites that come up... especially Islamic ones.
But scholars have noted, after reading some recently discovered manuscripts of Newton's work, that while Newton may have questioned the belief (as he apparently did most long-held beliefs), Newton's Arian tendencies may have been fleeting.
"I had no hesitation when writing the Life of Sir Isaac Newton in 1830, in coming to the conclusion that he was a believer in the Trinity; and in giving this opinion on the creed of so great a man, and so indefatigable a student of scripture, I was well aware that there are various forms of Trinitarian truth, and various modes of expressing it, which have been received as orthodox in the purest societies of the Christian Church." Pfizenmaier, Thomas C. "Was Isaac Newton an Arian?", Journal of the History of Ideas - Volume 58, Number 1, January 1997, pp. 57-80Finally, I'd like to note one other thing the PBS show mentioned... Newton believed that theology and science were intricately connected. Newton's calculus, law of gravity, motion of planets and theories about light belonged not to a universe free from the control of God, but were evidences of His providential hand. While Newton came upon these discoveries in an emperical manner, he none-the-less seemed to believe he was peering into mysterious handiwork of God. Newton argued that one could not understand the universe apart from the existence of God, not just a god, but clearly in Newton's view, the God of the Bible, regardless of his views on the Trinity.
If you have any other resources regarding Newton's theological writings and views, please mention them in the comments! Thanks!